Problem: Solve for $a$. Give an exact answer. $3+0.5(4a+8)=9-2a$ $a =$
We need to manipulate the equation to get $ a $ by itself. $\begin{aligned} 3+0.5(4a+8) &= 9-2a \\\\ 3+2a+4 &= 9-2a~~~~~~~~~~\gray{\text{Distribute}}\\\\ 2a+7 &= 9-2a~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2a+7{+2a} &= 9-2a{+2a} ~~~~~~~~~~\gray{\text{Add 2a to each side}}\\\\ 4a+7 &= 9~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 4a+7{-7} &=9 {-7} ~~~~~~~~~~\gray{\text{Subtract 7 from each side}}\\\\ 4a &=2 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{4a}{{4}}&= \dfrac{2}{{4}}~~~~~~~~~~\gray{\text{Divide each side by 4}} \\\\ a &= {0.5} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ a= { 0.5 }~~~~~~~~$ [Let's check our work!]